country
$20 Bonus + 25% OFF
Securing Higher Grades Costing Your Pocket? Book Your Assignment at The Lowest Price Now!
Add File

Error goes here

Arithmetic Sequences And Their Properties

Referencing Styles : APA | Pages : 1

Arithmetic sequences:

An arithmetic sequence is defined as a list of numbers having a definite pattern. Arithmetic sequences are developed such that when the numbers are taken in sequence they can be subtracted by its previous number, the result always remains the same. The difference that exists between all the pairs of consecutive or successive numbers within a sequence is known as the common differences that are usually denoted by the letter “d”. The common difference is used in order to go from one term ti the other. The current term gets added up to the common difference in order to get the next number and this way the sequence carries on. Some of the facts that fall under the arithmetic sequences are as follows:

  • When the common difference between two consecutive terms is positive, the sequence is said to be increasing in nature.
  • When the common difference between two consecutive terms is negative then the arithmetic sequence is said to be decreasing in nature.

Thus it can be said that arithmetic sequence is a set of numbers which gradually increases or decreases by a constant amount for each term.

The formula for the nth term of a sequence in arithmetic is given in the following form:

an=dn+c

Here d is defined as the common difference

Once the common difference between the numbers is identified, the value of c can be easily plugged in 1 for n where the first term of the sequence is denoted by a1.

Some of the examples of arithmetic sequence re as follows:

1. {1,5,9,13,17,21,25,...}

Since, 5-1= 4

9-5=4 etc

Therefore, the common difference between the numbers is calculated as 4

25 + 4 = 29

29 + 4 = 33

33 + 4 = 37

Hence the next 3 terms will be 29, 33 and 37.

In order to find the nth term we can use the formula for arithmetic sequence while substituting the value by n=1,a1=1n=1,a1=1 and d=4d=4 in the formula of an=dn+c

Using this formula will help in finding c.

Hence, 1=4(1)+c

c=−3

Therefore a formula for the nth term of the arithmetic sequence is

an=4n−3.

2. {12,9,6,3,0,−3,−6,...}

Since 9 -12 = -3

6 – 9 = - 3 and so on hence the common difference of the arithmetic sequence is -3.

It is worthy to be noted here that since the sequence is decreasing in nature the common difference is negative.

In order to find the next 3 terms, it is required to subtract by 3.

-6 – 3 = - 9

-9 – 3 = - 12

-12 – 3 = -15

Hence the next three terms will be -9, -12, and  -15.

Replacing the values we get the desired result of c as below:

12 = -3 (1) + c

c = 15

Hence from the formula, the nth term of the sequence is

an=−3n+15.

Properties of Arithmetic sequences:

The property of arithmetic sequence is as follow:

1. If a constant gets added to each of the terms of an arithmetic sequence then the resulting sequence is also an arithmetic sequence.

2. If a constant gets subtracted from each of the term of an Arithmetic sequence then the resulting sequence will also be an arithmetic sequence.

3. If each term of an arithmetic sequence is multiplied by a constant then the resulting sequence will also be an arithmetic sequence.

4. If each term of an arithmetic sequence is divided by a constant then the resulting sequence will also be an arithmetic sequence.

5. If the nth term is in linear form then sequence will be in A.P.

Solutions

OR

Specially designed essay help services have made MyAssignmenthelp.com one of the most prolific proposal essay help providers. We have arrays of expert essay writers who successfully deliver essay help depending on broad ranges of subjects and topics. We provide nursing essay help, MBA essay help, English Essay writing help and law essay help to students from different fields of study. Broad ranges of essay writing services assist us to offer quality contents within a specific time limit.

Save Time & improve Grade

Just share requirement and get customized Solution.

watch
question
We will use e-mail only for:

arrow Communication regarding your orders

arrow To send you invoices, and other billing info

arrow To provide you with information of offers and other benefits

Add File

Error goes here

1,545,015

Orders

4.9/5

Overall Rating

5,108

Experts

Our Amazing Features

delivery

On Time Delivery

Our writers make sure that all orders are submitted, prior to the deadline.

work

Plagiarism Free Work

Using reliable plagiarism detection software, Turnitin.com.We only provide customized 100 percent original papers.

time

24 X 7 Live Help

Feel free to contact our assignment writing services any time via phone, email or live chat. If you are unable to calculate word count online, ask our customer executives.

subject

Services For All Subjects

Our writers can provide you professional writing assistance on any subject at any level.

price

Best Price Guarantee

Our best price guarantee ensures that the features we offer cannot be matched by any of the competitors.

Our Experts

Assignment writing guide
student rating student rating student rating student rating student rating 5/5

647 Order Completed

98% Response Time

Adlina Han

Masters in Marketing with Specialization in Branding

Singapore, Singapore

Hire Me
Assignment writing guide
student rating student rating student rating student rating student rating 5/5

285 Order Completed

99% Response Time

Eugene Baranowski

MBA in Supply Chain

London, United Kingdom

Hire Me
Assignment writing guide
student rating student rating student rating student rating student rating 5/5

610 Order Completed

100% Response Time

Cheryl Zhao

PhD in Statistics

Singapore, Singapore

Hire Me
Assignment writing guide
student rating student rating student rating student rating student rating 5/5

93 Order Completed

100% Response Time

Jackson Mitchell

MiM (Masters in Management) in Supply Chain Management

New Jersey, United States

Hire Me

FREE Tools

plagiarism

Plagiarism Checker

Get all your documents checked for plagiarism or duplicacy with us.

essay

Essay Typer

Get different kinds of essays typed in minutes with clicks.

edit

GPA Calculator

Calculate your semester grades and cumulative GPa with our GPA Calculator.

referencing

Chemical Equation Balancer

Balance any chemical equation in minutes just by entering the formula.

calculator

Word Counter & Page Calculator

Calculate the number of words and number of pages of all your academic documents.

Refer Just 5 Friends to Earn More than $2000

Check your estimated earning as per your ability

1

1

1

Your Approx Earning

Live Review

Our Mission Client Satisfaction

An efficient writing assignment service that comes at a reasonable price. It will never let you down. Very satisfied with the service.

flag

User Id: 312798 - 18 Jan 2021

Australia

student rating student rating student rating student rating student rating

Very fast work and really academic. The proffessor not using very professional words in case that will cause some problems with us. The assignment satisfy all the requirement! It\'s cost-effective!

flag

User Id: 581460 - 18 Jan 2021

Australia

student rating student rating student rating student rating student rating

Great service with friendly staff. they prepare good solutions in a fair period of time. recommended.

flag

User Id: 444979 - 18 Jan 2021

Australia

student rating student rating student rating student rating student rating

Thank You very much for the help. You guys are really amazing. Looking forward to working with you soon.

flag

User Id: 272706 - 18 Jan 2021

Australia

student rating student rating student rating student rating student rating
Arithmetic Sequences And Their... has been added in your library.
callback request mobile
Have any Query?